Parallel simulation of transfer lines by time segmentation

This paper is concerned with the development of efficient parallel simulation techniques for an important class of manufacturing systems, namely Markovian transfer lines. The basic idea is to adapt the time segmentation parallel simulation method of Andradóttir and Ott, that was originally developed for parallel simulation of communication systems, to be used in this manufacturing setting. This is a challenging task because one of the key assumptions that the time segmentation method is based on (namely the monotonicity of sample paths) is violated in this context. We start by showing that a straightforward application of the time segmentation method to simulate transfer lines may involve some approximations, and include theoretical and numerical results that suggest that the effects of these approximations are minor. Then we present a generalization of the time segmentation method and show how this generalized version can be used to simulate transfer lines without any approximations. Next, we use numerical results to assess the efficiency of the two proposed variants of the time segmentation method. Finally, we show how the results in this paper can be used to generate unbiased observations from the steady-state distributions of Markovian transfer lines. In addition to the proposed approaches for simulating transfer lines, this paper contains new ideas that can be used to develop parallel simulation and unbiased steady-state simulation techniques for other applications. Our results also give new insights into the behavior of transfer lines.